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On universality for the kinetic wave equation

Pierre Germain, Hui Zhu

Abstract

On compact Riemannian manifolds with chaotic geometries, specifically those exhibiting the random wave model conjectured by Berry, we derive heuristically a homogeneous kinetic wave equation that is universal for all such manifolds.

On universality for the kinetic wave equation

Abstract

On compact Riemannian manifolds with chaotic geometries, specifically those exhibiting the random wave model conjectured by Berry, we derive heuristically a homogeneous kinetic wave equation that is universal for all such manifolds.
Paper Structure (20 sections, 54 equations)

This paper contains 20 sections, 54 equations.

Table of Contents

  1. Introduction
  2. The kinetic wave equation
  3. The random wave model
  4. Main result: kinetic limit on domains with chaotic geometries
  5. Discussion of the result
  6. Range of validity of the singular limit
  7. From (KW) to (KWR)
  8. Universality of turbulent spectra
  9. Questions
  10. The random wave model and its implications
  11. Berry's conjecture
  12. Weak formulation
  13. Interaction integrals
  14. Phase randomization
  15. Derivation of the kinetic wave equation
  16. ...and 5 more sections

Theorems & Definitions (1)

  • Conjecture 3.1: Berry